QuestionFind the coordinate of $P$ as the weighted average of points $A(-9, 2)$ and $D(2, 3)$ . Use an improper fraction if needed.

Studdy Solution

STEP 1

Assumptions1. Point A has a coordinate of -9 with a weight of. . Point D has a coordinate of with a weight of3.
3. The weighted average of a set of points is calculated by multiplying each point's coordinate by its weight, adding these products together, and then dividing by the sum of the weights.

STEP 2

First, we need to find the weighted sum of the coordinates. This is done by multiplying each coordinate by its weight and then adding these products together.
$Weighted\, sum = (Coordinate\, of\, A \\times Weight\, of\, A) + (Coordinate\, of\, D \\times Weight\, of\, D)$

STEP 3

Now, plug in the given values for the coordinates and weights of points A and D to calculate the weighted sum.
$Weighted\, sum = (-9 \\times2) + (2 \\times3)$

STEP 4

Calculate the weighted sum.
$Weighted\, sum = -18 +6 = -12$

STEP 5

Now that we have the weighted sum, we can find the weighted average by dividing the weighted sum by the total weight. The total weight is the sum of the weights of points A and D.
$Weighted\, average = Weighted\, sum / Total\, weight$

STEP 6

Calculate the total weight.
$Total\, weight = Weight\, of\, A + Weight\, of\, D =2 +3 =5$

STEP 7

Now, plug in the values for the weighted sum and the total weight to calculate the weighted average.
$Weighted\, average = -12 /5$

STEP 8

The coordinate of point that represents the weighted average of the set of points is -12/5.
Point has a coordinate of -12/5.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms